The idealized GCM with the simple quasi-equilibrium convection scheme has been used in numerous studies of large-scale atmosphere dynamics and mechanisms of climate changes, especially those involving the hydrologic cycle e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}. We know from this body of work that the convection scheme primarily affects the atmospheric thermal stratification in the tropics, with weaker effects in the extratropics [14]}. We also know that the relative humidity parameter (RH) in the moist convection scheme controls the humidity of the tropical free troposphere but likewise has a weaker effect on the humidity of the extratropical free troposphere [15]}. Thus, we expect tropical circulation statistics to be especially informative about the parameters in the convection scheme. However, convection plays a central role in extreme precipitation events at all latitudes [4]}, [17]}, so we expect statistics of precipitation extremes to be informative about convective parameters, and in particular to contain information about the relaxation timescale \(\tau \) .
